The articles and essays in this blog range from the short to the long. Many of the posts are also introductory (i.e., educational) in nature; though, even when introductory, they still include additional commentary. Older material (dating back mainly to 2005) is being added to this blog over time.

Wednesday, 9 September 2015

The Fundamental Nature of Modus Ponens

In
terms of Quine’s web of belief, and the thesis that observation or
experience may lead us to change our logic (or to change classical
logic), Hartry Field argues that

“one
is likely to need modus ponens
in the background logic in which one reasons about what follows from
each theory-plus-logic and how well it accords with observations”;
and it is hard to imagine that a person using this background logic
could rationally come to favour a theory-plus-logic in which the
logic conflicted with the background logic.”[2000]

To
be clear about Field’s position, it boils down to two points:

i) It's likely that modus
ponens will be used in the ‘background’ logic to reason about
what changes one should make to the logic (or logics) contained in
the web of belief.

ii) The background logic
won't allow us to come to the conclusion that our ‘new’ logic
conflicts or negates that very same background logic (which includes
modus ponens).

Paul
Boghossian also offers the intuitively plausible position

“that
it is not possible for us to be justified in believing something as
basic as modus ponens”.[2000]

Well,
if modus ponens (MP) is the most fundamental rule of inference
then it is indeed basic.

Does
that basic nature of MP automatically mean that it's not possible for
us to justify it? Does that fundamentality simply amount to the fact
that we must use MP in our justifications of MP? That in itself
doesn't show us that it can’t be justified or that it's indeed
basic. Perhaps it's not as basic as it seems anyway. It may have
hidden complexity or structure.

Boghossian
still asks:

“For
in what could such a justification consist?”

It
can't be more basic than MP because there's no rule of inference more
basic than MP. So either MP must be justified using MP or be
justified by other rules of inference which are themselves derived
from MP.

So
far we've only talked about the difficulty (or impossibly!) of
escaping from MP. However, we may still need to justify it.
Nonetheless, if MP

“is
unjustifiable, then so is anything that is based on it, and that
would appear to include any belief whose justification is deductive”.[2000]

Not
only is MP the most basic form of inference: it's the case that just
about every belief is based on it (in some direct or indirect way)
because it will include something that is itself deductive.

Thus
any scepticism about MP will itself will be based on MP (as well as
on other) deductions. Thus a belief in the lack of justification for
MP will itself be unjustified or unjustifiable (if only from a
logical point of view).

Thus
that sceptical conclusion has this form:

P
→ QPQ

Or:

i) If modus ponens
isn't justified, then there's no reason to use/accept it.